TY - JOUR
T1 - A Bayesian Approach to Sequential Optimization based on Computer Experiments
AU - Tajbakhsh, Sam Davanloo
AU - Del Castillo, Enrique
AU - Rosenberger, James Landis
N1 - Publisher Copyright:
Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2014 John Wiley & Sons, Ltd.
PY - 2015/10/1
Y1 - 2015/10/1
N2 - Computer experiments are used frequently for the study and improvement of a process under study. Optimizing such process based on a computer model is costly, so an approximation of the computer model, or metamodel, is used. Efficient global optimization (EGO) is a sequential optimization method for computer experiments based on a Gaussian process model approximation to the computer model response. A long-standing problem in EGO is that it does not consider the uncertainty in the parameter estimates of the Gaussian process. Treating these estimates as if they are the true parameters leads to an improper assessment of the precision of the approximation, a precision that is crucial to assess not only in optimization but in metamodeling in general. One way to account for these uncertainties is to use bootstrapping, studied by previous authors. Alternatively, some other authors have mentioned how a Bayesian approach may be the best way to incorporate the parameter uncertainty in the optimization, but no fully Bayesian approach for EGO has been implemented in practice. In this paper, we present a fully Bayesian implementation of the EGO method. The proposed Bayesian EGO algorithm is validated through simulation of noisy nonlinear functions and compared with the standard EGO method and the bootstrapped EGO. We also apply the Bayesian EGO algorithm to the optimization of a stochastic computer model. It is shown how a Bayesian approach to EGO allows one to optimize any function of the posterior predictive density.
AB - Computer experiments are used frequently for the study and improvement of a process under study. Optimizing such process based on a computer model is costly, so an approximation of the computer model, or metamodel, is used. Efficient global optimization (EGO) is a sequential optimization method for computer experiments based on a Gaussian process model approximation to the computer model response. A long-standing problem in EGO is that it does not consider the uncertainty in the parameter estimates of the Gaussian process. Treating these estimates as if they are the true parameters leads to an improper assessment of the precision of the approximation, a precision that is crucial to assess not only in optimization but in metamodeling in general. One way to account for these uncertainties is to use bootstrapping, studied by previous authors. Alternatively, some other authors have mentioned how a Bayesian approach may be the best way to incorporate the parameter uncertainty in the optimization, but no fully Bayesian approach for EGO has been implemented in practice. In this paper, we present a fully Bayesian implementation of the EGO method. The proposed Bayesian EGO algorithm is validated through simulation of noisy nonlinear functions and compared with the standard EGO method and the bootstrapped EGO. We also apply the Bayesian EGO algorithm to the optimization of a stochastic computer model. It is shown how a Bayesian approach to EGO allows one to optimize any function of the posterior predictive density.
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U2 - 10.1002/qre.1658
DO - 10.1002/qre.1658
M3 - Article
AN - SCOPUS:84942234898
SN - 0748-8017
VL - 31
SP - 1001
EP - 1012
JO - Quality and Reliability Engineering International
JF - Quality and Reliability Engineering International
IS - 6
ER -